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An analytical general analysis of the electromagnetic Dyadic Greens Function for two-dimensional sheet (or a very thin film) is presented, with an emphasis on on the case of graphene. A modified steepest descent treatment of the fields from a point dipole given in the form of Sommerfeld integrals is performed. We sequentially derive the expressions for both out-of-plane and in-plane fields of both polarizations. It is shown that the analytical approximation provided is very precise in a wide range of distances from a point source, down to a deep subwavelength region (1/100 of wavelength). We separate the contribution from the pole, the branch point and discuss their interference. The asymptotic expressions for the fields are composed of the plasmon, Norton wave and the components corresponding to free space.
We study the electronic structure of graphene with a single substitutional vacancy using a combination of the density-functional, tight-binding, and impurity Greens function approaches. Density functional studies are performed with the all-electron s
An analytical method for diffraction of a plane electromagnetic wave at periodically-modulated graphene sheet is presented. Both interface corrugation and periodical change in the optical conductivity are considered. Explicit expressions for reflecti
We present a numerically efficient technique to evaluate the Greens function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or `patches, are connected using self energy terms which
We present a further development of methods for analytical calculations of Greens functions of lattice fermions based on recurrence relations. Applying it to tight-binding systems and topological superconductors in different dimensions we obtain a nu
The boundary Greens function (bGF) approach has been established as a powerful theoretical technique for computing the transport properties of tunnel-coupled hybrid nanowire devices. Such nanowires may exhibit topologically nontrivial superconducting